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Find the greatest common factor of 63 and 42.
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Before we can find the greatest common factor of 63 and 42, we just need to find the factors of 63 and 42.
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Let’s do this by creating a factor tree.
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Factors of 63 are of course one and 63.
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Also I recognize that 63 is divisible by three.
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Three times 21 equals 63.
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21 is also divisible by three.
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Three times seven equals 21.
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Let’s do the same thing with 42.
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One times 42 equals 42.
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Two times 21 equals 42.
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21 is divisible by three.
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Three times seven equals 21.
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Now what we’re going to do is we’re going to write out all the prime factors of 63 and 42.
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63 equals one times three times three times seven.
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42 equal one times two times three times seven.
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The next thing that we’re going to do is we’re going to circle all the shared prime factors, all the prime factors that are found on both lists.
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Both 42 and 63 have a prime factor of three.
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Both 63 and 42 have a prime factor of seven.
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Three times seven is 21, and that makes 21 the greatest common factor of 63 and 42.
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Using prime factorization, we found all the common prime factors, multiplied those together to give us the greatest common factor of 63 and 42; it’s 21.